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arXiv · 2603.06033

Oort's conjecture on automorphisms of generic supersingular abelian varieties

Eva Viehmann
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Abstract

We prove Oort's conjecture that generically on the supersingular locus of the moduli space of principally polarized abelian varieties of genus g and in characteristic p, the automorphism group of the universal principally polarized abelian variety consists only of $\pm 1$, unless g=2 or 3 and p=2. On the way, we provide an explicit description of the a=1-locus in the Rapoport-Zink space of principally polarized supersingular p-divisible groups of any dimension g. We also prove analogous results for generic automorphism groups on moduli spaces of supersingular p-divisible groups with and without polarization.

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Eva Viehmann. 2026-03-06. Oort's conjecture on automorphisms of generic supersingular abelian varieties. https://arxiv.org/abs/2603.06033

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